If Bob is not profit oriented, he can max out his production thus maximize the social wealth, but he won't have enough motivation to do so, since redistributing his products to Alice is more like a donation. Money is that motivation: If Bob can exchange all his production into money, he has some motivation to produce more, since money will store value and delay his consumption until a later time. Unfortunately, since Alice have little access to money, Bob can not make money by himself alone
Robinson Crusoe fallacy.
If they are only 2 people or even a hundred people. They are going to collaborate not compete if they want to survive
We are talking about high productivity here, with the help of technology, Bob does not need to cooperate with Alice, but he need Alice to buy his products with money, this is a strange but prevail culture on this planet
Two people's island is just a metaphor, it involves the basic elements in today's society: Production, exchange and consumption. In such a society, each one must find his customer to sell his products/services, a model of two person is enough to represent the whole society